Question: Solve for $x$ and $y$ by deriving an expression for $y$ from the second equation, and substituting it back into the first equation. $\begin{align*}-2x-3y &= -8 \\ -8x+9y &= 4\end{align*}$
Begin by moving the $x$ -term in the second equation to the right side of the equation. $9y = 8x+4$ Divide both sides by $9$ to isolate $y$ $y = {\dfrac{8}{9}x + \dfrac{4}{9}}$ Substitute this expression for $y$ in the first equation. $-2x-3({\dfrac{8}{9}x + \dfrac{4}{9}}) = -8$ $-2x - \dfrac{8}{3}x - \dfrac{4}{3} = -8$ Simplify by combining terms, then solve for $x$ $-\dfrac{14}{3}x - \dfrac{4}{3} = -8$ $-\dfrac{14}{3}x = -\dfrac{20}{3}$ $x = \dfrac{10}{7}$ Substitute $\dfrac{10}{7}$ for $x$ back into the top equation. $-2( \dfrac{10}{7})-3y = -8$ $-\dfrac{20}{7}-3y = -8$ $-3y = -\dfrac{36}{7}$ $y = \dfrac{12}{7}$ The solution is $\enspace x = \dfrac{10}{7}, \enspace y = \dfrac{12}{7}$.